ComputeSoup – Web Computational Engine

(Equation/Expression Evaluation)

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AreaCircle( radius ):
Area of the circle with radius radius. AreaCircle(r) =
πr²

Yes

AreaCone

2

1

AreaCone( radius, height
): Area of a right cone of radius
radius and height height
(does not include the base).
AreaCone(r,h) = πr√r² +
h²

Yes

AreaCube

1

1

AreaCube( side ):
Area of a cube of side side.
AreaCube(s) = 6s²

Yes

AreaCylinder

2

1

AreaCylinder( radius, height
): Area of a right cylinder of radius
radius and height height
(does not include base, top).
AreaCylinder(r,h) =
2πrh

Yes

AreaEllipse

2

1

AreaEllipse( axis1, axis2
): Area of an ellipse with semiaxes of
axis1 and axis2
AreaEllipse(a,b) = πab

Yes

AreaFrustum

3

1

AreaFrustum( baseRadius,
topRadius, height ): Area of the curved surface
of the frustum of a right cone with base radius
baseRadius, top radius topRadius,
and height height
AreaFrustum(b,t,h) = π(b+t)√h²+(b–t)²

Yes

Function

Args

Results

Prototype/Description

Expr Use?

AreaLune

2

1

AreaLune( radius, inclination
): Area of a lune on the surface of a sphere of
radius radius included between two great circles
whose inclination is inclination degrees:
AreaLune(r,A) =
2πr²A/180

Yes

AreaOblSpheroid

2

1

AreaOblSpheroid( majorSemiAxis,
minorSemiAxis ): Given an ellipse with major
semiaxis majorSemiAxis and minor semiaxis
minorSemiAxis, with (majorSemiAxis
> minorSemiAxis), an oblate spheroid is
formed by the rotation of the ellipse about its minor axis.
The surface area of an oblate spheroid is given
by: AreaOblSpheroid(a,b) =
π((2a²+(b²/E)*Ln((1+E)/(1–E)))where E
(Eccentricity) is: E = √a²–b² /a

Yes

AreaProlSpheroid

2

1

AreaProlSpheroid( majorSemiAxis,
minorSemiAxis ): Given an ellipse with major
semiaxis majorSemiAxis and minor semiaxis
minorSemiAxis, with
(majorSemiAxis >
minorSemiAxis), a prolate spheroid is formed by
the rotation of the ellipse about its major axis. The
surface area of an prolate spheroid is given by:
AreaProlSpheroid(a,b) =
2π(b²+(ab*Asin(E)/E))where E (Eccentricity)
is: E = √a²–b² /a

Yes

AreaPyramid

3

1

AreaPyramid( nSides, base,
height ): Lateral area of a regular pyramid of
nSides sides, base dimension base
(length of one side of base), and slant height
height AreaPyramid(n,b,h)
= ½nbh

Yes

AreaRectangle

2

1

AreaRectangle( length, width
): Area of of a rectangle of sides
length and width
AreaRectangle(l,w) = lw

Yes

AreaRegPolygon

2

1

AreaRegPolygon( nSides,
length ): Area of a regular polygon with
nSides sides, each of length
length. See also RegPolygon()
AreaRegPolygon(n,L) =
nL²/(4tan(π/n))

Yes

AreaSphere

1

1

AreaSphere( radius ):
Area of a sphere of radius radius
AreaSphere(r) =
4πr²

Yes

AreaSphPolygon

3

1

AreaSphPolygon( radius, nSides,
angleSum ): Area of a spherical polygon of
nSides sides, where angleSum is
sum of its angles (degrees), and radius is the
sphere's radius:
AreaSphPolygon(r,n,S)
= πr²((S/180)–(n–2)))

ArithmeticLast( firstTerm, delta,
numb ): The last element in the Arithmetic
Progression defined by its first term
(firstTerm), delta (delta), and
number of elements (numb)
ArithmeticLast(a,d,n) = a+(n–1)d

Yes

Function

Args

Results

Prototype/Description

Expr Use?

ArithmeticSum

3

1

ArithmeticSum( firstTerm, delta,
numb ): The sum of the elements in the
Arithmetic Progression defined by its first term
(firstTerm), delta (delta), and
number of elements (numb)
Eq. 1 ArithmeticSum(a,d,n) =
½n(2a+(n–1)d);
Note that if the last term is L, the sum may be computed
as: Eq. 2 ArithmeticSum(a,n,L)
= ½n(a+L); This program uses only Equation (1)
above

Yes

Asin

1

1

Asin( x ): Arcsine
of x, (–1 ≤
x ≤ 1)

Yes

Asinh

1

1

Asinh( x ): Arc
hyperbolic sine of x
Asinh(x) = Ln(x + √1+x² )

Yes

Atan

1

1

Atan( x ):
Arctangent of x

Yes

Atan2

2

1

Atan2( x, y ):
Arctangent of x/y (x
= y = 0 is illegal). Atan2() overcomes
a limitation with Atan(). Specifically, with two
arguments, Atan2() can return the angle in the correct
quadrant

BillSplit( bill, nShares,
tipPercent ): The (rounded) amount each of
nShares people should pay towards a total bill
of (bill + tip), where tip is
tipPercent of bill. Note
that (nShares > 1) and need not be an integer,
and (0 ≤ tipPercent ≤ 100).
See also Tip().

No

Binary

1

1

Binary( int ):
Display the integer argument int
in binary

No

BitCount

1

1

BitCount( int ):
Return the number of 1 bits in the 32-bit integer
argument int. Same as PopCount()